Do you know its property ?-7

We have $x+y+z \le 1729$ .

$\Rightarrow 1729-(x+y+z) \ge 0$

Let $1729-(x+y+z)=w$ where it is clear that w is also an integer.

We have to find number of non-negative integral solutions of :

$x+y+z+w=1729$

We know number of integral solutions of :

${x}_{1}+{x}_{2}+.........{x}_{n}=r$ is given by :

$=^{n+r-1}{C}_{r}$

Applying this property we have :

No of integral solutions: $^{1732}{C}_{3}=864449860$